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207. Course Schedule

Medium

There are a total of numCourses courses you have to take, labeled from 0 to numCourses - 1. You are given an array prerequisites where prerequisites[i] = [ai, bi] indicates that you must take course bi first if you want to take course ai.

• For example, the pair [0, 1], indicates that to take course 0 you have to first take course 1.

Return true if you can finish all courses. Otherwise, return false.

Example 1:

Input: numCourses = 2, prerequisites = [[1,0]]

Output: true

Explanation: There are a total of 2 courses to take. To take course 1 you should have finished course 0. So it is possible.

Example 2:

Input: numCourses = 2, prerequisites = [[1,0],[0,1]]

Output: false

Explanation: There are a total of 2 courses to take. To take course 1 you should have finished course 0, and to take course 0 you should also have finished course 1. So it is impossible.

Constraints:

• 1 <= numCourses <= 105
• 0 <= prerequisites.length <= 5000
• prerequisites[i].length == 2
• 0 <= ai, bi < numCourses
• All the pairs prerequisites[i] are unique.

Solution

const WHITE = 0
const GRAY = 1
const BLACK = 2

function canFinish(numCourses: number, prerequisites: number[][]): boolean {
    const adj: number[][] = Array.from({ length: numCourses }, () => [])
    for (const pre of prerequisites) {
        adj[pre[1]].push(pre[0])
    }
    const colors: number[] = new Array(numCourses).fill(WHITE)
    for (let i = 0; i < numCourses; i++) {
        if (colors[i] === WHITE && adj[i].length > 0 && hasCycle(adj, i, colors)) {
            return false
        }
    }
    return true
}

function hasCycle(adj: number[][], node: number, colors: number[]): boolean {
    colors[node] = GRAY
    for (const nei of adj[node]) {
        if (colors[nei] === GRAY) {
            return true
        }

        if (colors[nei] === WHITE && hasCycle(adj, nei, colors)) {
            return true
        }
    }
    colors[node] = BLACK
    return false
}

export { canFinish }

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